Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 1—Description of the Method

1993 ◽  
Vol 115 (1) ◽  
pp. 94-100 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Boundary Layer ◽  
Numerical Test ◽  
Unsteady Flows ◽  
Boundary Layer Separation ◽  
Displacement Effect ◽  
Integral Boundary ◽  
Time Resolved ◽  
Boundary Layer Equations ◽  
Momentum Integral ◽  
Viscous Solutions

An efficient coupled approach between inviscid Euler and integral boundary layer solutions has been developed for quasi-3-D unsteady flows induced by vibrating blades. For unsteady laminar and turbulent boundary layers, steady correlations are adopted in a quasi-steady way to close the integral boundary layer model. This quasi-steady adoption of the correlations is assessed by numerical test results using a direct solution of the unsteady momentum integral equation. To conduct the coupling between the inviscid and viscous solutions for strongly interactive flows, the unsteady Euler and integral boundary layer equations are simultaneously time-marched using a multistep Runge–Kutta scheme, and the boundary layer displacement effect is accounted for by a first order transpiration model. This time-resolved coupling method converges at conditions with considerable boundary layer separation.

Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 1 — Description of the Method

1991 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Boundary Layer ◽  
Numerical Test ◽  
Unsteady Flows ◽  
Boundary Layer Separation ◽  
Displacement Effect ◽  
Integral Boundary ◽  
Time Resolved ◽  
Boundary Layer Equations ◽  
Momentum Integral ◽  
Viscous Solutions

An efficient coupled approach between inviscid Euler and integral boundary layer solutions has been developed for quasi 3-D unsteady flows induced by vibrating blades. For unsteady laminar and turbulent boundary layers, steady correlations are adopted in a quasi-steady way to close the integral boundary layer model. This quasi-steady adoption of the correlations is assessed by numerical test results using a direct solution of the unsteady momentum integral equation. To conduct the coupling between the inviscid and viscous solutions for strongly interactive flows, the unsteady Euler and integral boundary layer equations are simultaneously time-marched using a multi-step Runge-Kutta scheme, and the boundary layer displacement effect is accounted for by a first order transpiration model. This time-resolved coupling method converges at conditions with considerable boundary layer separation.

An Accurate Calculation Method for Two-dimensional Incompressible Laminar Boundary Layers, Including Cases with Regions of Sharp Pressure Gradient

1977 ◽  
Vol 28 (3) ◽  
pp. 149-162 ◽  
Author(s):  
N Curle
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Calculation Method ◽  
Boundary Layer Separation ◽  
Pressure Gradients ◽  
Accurate Calculation ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Type Boundary

SummaryThe paper develops and extends the calculation method of Stratford, for flows in which a Blasius type boundary layer reacts to a sharp unfavourable pressure gradient. Whereas even the more general of Stratford’s two formulae for predicting the position of boundary-layer separation is based primarily upon an interpolation between only three exact solutions of the boundary layer equations, the present proposals are based upon nine solutions covering a much wider range of conditions. Four of the solutions are for extremely sharp pressure gradients of the type studied by Stratford, and five are for more modest gradients. The method predicts the position of separation extremely accurately for each of these cases.The method may also be used to predict the detailed distributions of skin friction, displacement thickness and momentum thickness, and does so both simply and accurately.

Transonic Compressor Rotor Cascade With Boundary-Layer Separation: Experimental and Theoretical Results

1993 ◽  
Author(s):  
R. Fuchs ◽  
W. Steinert ◽  
H. Starken
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Computational Design ◽  
Boundary Layer Separation ◽  
Ratio Test ◽  
Integral Boundary ◽  
Flow Angle ◽  
Laminar Separation ◽  
Transonic Compressor ◽  
Compressor Rotor

A transonic compressor rotor cascade designed for an inlet Mach number of 1.09 and 14 degrees of flow turning has been redesigned for higher loading by an increased pitch-to-chord ratio. Test results, showing the influence of inlet Mach number and flow angle on cascade performance are presented and compared to data of the basic design. Loss-levels of both, the original and the redesigned higher loaded blade were identical at design condition, but the new design achieved even lower losses at lower inlet Mach numbers. The computational design and analysis has been performed by a fast inviscid time-dependent code coupled to a viscous direct/inverse integral boundary-layer code. Good agreement was achieved between measured and predicted surface Mach number distributions as well as exit-flow angles. A boundary-layer visualization method has been used to detect laminar separation bubbles and turbulent separation regions. Quantitative results of measured bubble positions are presented and compared to calculated results.

On the interaction between shock waves and boundary layers

1951 ◽  
Vol 47 (3) ◽  
pp. 545-553 ◽  
Author(s):  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Shock Waves ◽  
Boundary Layers ◽  
Weak Shock ◽  
Boundary Layer Separation ◽  
Weak Shock Wave ◽  
Layer Separation ◽  
Boundary Layer Equations

AbstractThe effect on the boundary-layer equations of a weak shock wave of strength ∈ has been investigated, and it is shown that ifRis the Reynolds number of the boundary layer, separation occurs when ∈ =o(R−i). The boundary-layer assumptions are then investigated and shown to be consistent. It is inferred that separation will occur if a shock wave meets a boundary and the above condition is satisfied.

Studies on boundary-layer separation in unsteady flows using an integral method

1984 ◽  
Vol 149 (-1) ◽  
pp. 477 ◽  
Author(s):  
Michinori Matsushita ◽  
Shigeru Murata ◽  
Teruaki Akamatsu
Keyword(s):  
Boundary Layer ◽  
Integral Method ◽  
Unsteady Flows ◽  
Boundary Layer Separation ◽  
Layer Separation

Momentum Integral for Curved Shear Layers

1975 ◽  
Vol 97 (2) ◽  
pp. 253-256 ◽  
Author(s):  
Ronald M. C. So
Keyword(s):  
Boundary Layer ◽  
Shear Layers ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Displacement Effect ◽  
Curved Boundary ◽  
Curvature Effects ◽  
Von Karman ◽  
Momentum Integral ◽  
Von Kármán

If the exact metric influence of curvature is retained and the displacement effect neglected, it can be shown that the momentum integral for two-dimensional, curved boundary-layer flows is identical to the von Karman momentum integral. As a result, attempts by previous researchers to account for longitudinal curvature effects by adding more terms to the momentum integral are shown to be correct.

Numerical Solution of Laminar Boundary Layer Flow About a Rotating Sphere in an Axial Stream

1985 ◽  
Vol 107 (1) ◽  
pp. 97-104 ◽  
Author(s):  
M. A. I. El-Shaarawi ◽  
M. F. El-Refaie ◽  
S. A. El-Bedeawi
Keyword(s):  
Boundary Layer ◽  
Present Scheme ◽  
Rotating Sphere ◽  
Boundary Layer Equations ◽  
Meridional Velocity ◽  
Axis Of Rotation ◽  
Stress Components ◽  
Layer Flow ◽  
Momentum Integral ◽  
Uniform Stream

A finite-difference scheme is developed for solving the boundary layer equations governing the laminar flow about a rotating sphere which is subjected to a uniform stream in the direction of the axis of rotation. Numerical results are presented for the meridional and azimuthal velocities and for the wall-shear-stress components. Also, the angle at which the meridional velocity gradient normal to the wall vanishes is given at values of the parameter Ta/Re2 ranged from zero (the stationary sphere case) to 10000. As compared with the momentum integral technique of Schlichting [8], the present scheme succeeded in obtaining solutions for very considerably larger values of the parameter Ta/Re2.

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